In NEAT, is it a good idea to give the same ID to node genes created from the same connection gene?
In NEAT, the innovation of a node does not affect the evolution directly. Only the connection genes and their innovation will matter. So you can simply have whole numbers as IDs under each Genome / Network.
--EDIT-- (Complete reasoning)
In the original paper, it is clearly stated that the nodes from the better genome is taken during crossover and then only the connections are cross-over'ed (in some method) and hence the innovation numbers for the connections. NEAT is connection-centric and does not care much about evolving nodes.
Adding to that from basic neural networks theory, the nodes will never matter in a neural network because all the calculation and the learning happens in the connections. Think about a regular feed-forward network. You only care about the weight matrix which is a property of the connections instead of the nodes though both are present. Similarly in a NEAT generated network, the nodes will not matter, as all the learning takes place in the way these nodes are connected and the weights of the network.
Further, the nodes list can easily be derived from the connection list and hence marking the connections, are enough.